Reinhart and Rogoff’s coding mistake: Much Ado About Nothing

This week saw a wide circulation of recent working paper by Thomas Herndon, Michael Ash and Robert Pollin, “Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff“, Working Paper Series Number 322, Political Economy Research Institute, University of Massachusetts Amherst. The authors challenge the findings in Carmen Reinhart and Kenneth Rogoff’s “Growth in a Time of Debt“, American Economic Review, Papers and Proceedings 100, 573-578. During their efforts to replicate Reinhart and Rogoff’s findings on the relationship between public debt and growth for 20 developed countries post-WWII, Herndon et al. received the original codes from Reinhart and Rogoff. Upon scrutiny, they discovered a coding error in the spreadsheet: Five countries were excluded entirely (the first five in the alphabetically sorted list of countries).

The impact of the mistake is that growth is overstated in two, and understated in one, of the four public debt categories considered by Reinhart and Rogoff. To be precise, the following table shows the difference between Reinhart and Rogoff’s (RR) published growth rates, and the ones using the corrections by Herndon et al. (corrections reported on page 7 in their working paper):

Ratio of public debt to GDP

<30%

30-60%

60-90%

>90%

Average GDP Growth, RR (2010)

4.1%

2.8%

2.8%

–0.1%

Average GDP Growth, RR (2010), corrected

4.0%

3.0%

2.8%

0.2%

You may rightfully wonder the fuss is all about. This table show, I my view, that the coding mistake does not change awfully much of RR’s findings. A mistake is unfortunate, of course, but they can happen, and it is great that Herndon et al. found it. RR agree to this in their online comment on Herndon et al. where they thank for the correction. Left here, there would have been no media storm, no explosions in the blogosphere, nothing. It would have been a valid correction of a result in a scientific journal. Not something anybody would notice outside narrow academic circles.

What happened then? a) The RR paper has been used by some politicians as ammunition to put forth austerity measures in high-debt countries. b) Herndon et al. present alternative average growth computations on newer data which bring the 0.2% in the lower right-hand corner of the table up to 2.2% (while adding slightly to the other growth rates). c) Most then conflate “alternative computations”, “new data” and “a mistake” into just “a mistake”. This is after all the most comprehensible concept of the three. And then, of course, there is a fantastic story to be told about famous economists whose incompetence with spreadsheets has led the world into fiscal policy disasters. And it has been told again and again.

Even two of the authors of Herndon et al. got caught up in all the excitement when Financial Times gave Robert Pollin and Michael Ash space to write on “Austerity after Reinhart and Rogoff“. They write:

“When we performed accurate recalculations using their dataset, we found that, when countries’ debt-to-GDP ratio exceeds 90 per cent, average growth is 2.2 per cent, not -0.1 per cent.”

Not so. You performed accurate calculations on another dataset using another method. As shown above the coding mistake is not an issue. But the readers love it, as they can again assert themselves that economists are fools who only manages to use Excel. (This format is of course chosen to make dissemination of the data as wide as possible on RR’s website for their “This Time is Different” book, but let us not spoil the fun.).

Maybe Pollin and Ash just echoed Leonato in “Much Ado About Nothing”:

“A victory is twice itself when the achiever brings home full numbers” – Leonato in Act I, Scene I of Shakespeare, W. (1599): “Much Ado About Nothing”

PS: Their new computations are interesting. Their new data they got from RR (and they thank them by referring to data not deemed reliable in 2010 as “selective exclusion”). Their alternative computations of averages are not more compelling than RR: They take average growth rates of countries in all the years when in a given debt category, and not by averaging countries’ average growth as RR do (there is no “correct” as opposed to “incorrect” here, but RR’s method avoids that some persistently debt-ridden countries get unduly high weight). RR also provide median growth rates, which may be the more relevant measure in such a small sample. It is 1.6% in RR (2010) for the >90% public debt/GDP category. Herndon et al. are silent on medians; cf. RRs response.